Overview

expoFitter is a specialized tool for visualizing and fitting non-linear electrophysiological data, built using R, shiny, and flexdashboard. Designed to model slow neuronal currents like the calcium-dependent potassium current (\(I_{KCa}\)), expoFitter provides robust methodologies for fitting and analyzing current kinetics through single- and double-exponential models. This allows researchers to extract time constants and assess model fitness, giving insight into current dynamics. While expoFitter does not directly measure intracellular calcium (\([Ca^{2+}]_i\)) dynamics, the tool’s modeling logic and uncovered temporal information has been effectively used as an indirect measure of \([Ca^{2+}]_i\) changes in neurons of the lobster pyloric network, as demonstrated in ongoing research (Ellison et al., in progress; Thuma et al., in progress). The tool’s robust non-linear least squares optimization makes it highly effective for studying slow electrophysiological processes.

Tool Features

• Data Preprocessing and Filtering: Incorporates a unique data wrangling/filtering algorithm that utilizes both finite and simple differentiation to extract salient parts of the current trace, ensuring accurate and reliable model fits. This preprocessing step is essential for isolating active portions of the current.

• Native Model Parameter Approximator: Integrates approximator functionality automating model initial-conditional estimates based on quintessential features of the experimental data. Given the robustness of the optimizer, this reduces the need for manual adjustment of these parameters by the user.

• Flexible and Robust Exponential Model Fitting: Supports both single- and double-exponential model fits using the nlsLM algorithm from the minpack.lm package. The nlsLM algorithm implements the Levenberg-Marquardt Algorithm, which combines gradient descent and the Gauss-Newton method for robust non-linear least squares optimization (see Supplemental Information below). The application fits experimental data using the following exponential models:

  • Single-Exponential Model:

  \[I = A e^{-\frac{t}{B}} + C\]

  • Double-Exponential Model:

  \[I = A e^{-\frac{t}{B}} + C e^{-\frac{t}{D}} + E\]

  where \(B\) and \(D\) represent the time constants of the first and second phase of the exponential curve, respectively.

• Interactive Visualization and Model Parameter Adjustment: Provides a fully interactive interface for data visualization and model fitting, enabling users to dynamically adjust model parameters through sliders and observe the resultant model solution both quantitatively and visually.

Installation

expoFitter Locally

There are several ways to access expoFitter. If you want the entirety of the repository, you can clone it to your local machine using these terminal commands (terminal used generically throughout):

git clone https://github.com/ryEllison/expoFitter.git
cd expoFitter

Ensure you are in the desired directory before executing the terminal commands. You can also use a point-and-click approach by navigating to Code in Github and selecting Download ZIP. Downloading expoFitter this way will require your moving expoFitter from your local Downloads to the desired location on your machine.

To run expoFitter locally, ensure that R is installed on your system, as well as the following packages:

• dplyr 1.1.4
• minpack.lm 1.2.4
• DT 0.33
• shiny 1.9.1

and your system’s environmental variables provide terminal access to R’s interpreter Rscript. Package installation is automated and can be completed by running the install_dependencies pseudo-executable in the \bin directory.

expoFitter can then be deployed utilizing your machine as a local server via the expoFitter_R pseudo-executable in the \bin directory. To make any tweaks or alterations to the tool to fit your particular use case, the code is dispersed throughout appropriate directories (e.g., \app, \scripts, and \src).

expoFitter as Electron App

expoFitter has also been built as a portable, desktop Electron app. The Electron build can be found in the \electron directory. However, for access to the desktop app the \installer directory can be downloaded using this terminal approach:

git clone --no-checkout https://github.com/ryEllison/expoFitter.git
cd expoFitter
git sparse-checkout init --cone
git sparse-checkout set ./installer
git checkout master
cd installer
pseudo_installer.bat

Again, ensuring you are in the directory where you wish the installer to be placed before executing the terminal commands.

You can also use a point-and-click approach and directly download the installer using the hyperlink below:

Installer

Downloading expoFitter this way will require your moving the installer from your local downloads to the desired location on your machine before executing the pseudo-installer pseudo-executable.

expoFitter on shinyapps.io

Lastly, expoFitter has been made publicly available as a web app, which is hosted on shinyapps.io, and can be accessed using https://ryellison.shinyapps.io/expofitter/.

Supplemental Information

Levenberg-Marquardt Algorithm

Update rule:

\[\mathbf{x}_{k+1} = \mathbf{x}_k - \left( \mathbf{J}^T \mathbf{J} + \lambda \mathbf{I} \right)^{-1} \mathbf{J}^T \mathbf{r}\]

Where:

• \(\mathbf{J}\) is the Jacobian matrix of the residuals,
• \(\mathbf{r}\) is the residual vector (differences between observed and predicted data),
• \(\lambda\) is a damping factor that controls the transition between gradient descent (for stability) and the Gauss-Newton method (for faster convergence).

Gradient Descent (when \(\lambda\) is large)

Update rule:

\[\mathbf{x}_{k+1} = \mathbf{x}_k - \alpha \nabla F(\mathbf{x}_k)\]

Where:

• \(\alpha\) is the learning rate,
• \(\nabla F\) is the gradient of the cost function.

Gauss-Newton Method (when \(\lambda\) is small)

Update rule:

\[\mathbf{x}_{k+1} = \mathbf{x}_k - \left( \mathbf{J}^T \mathbf{J} \right)^{-1} \mathbf{J}^T \mathbf{r}\]

These methods ensure high-fidelity parameter estimation for complex neuroelectrophysiological datasets.